# Pythagorean identities

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• Apr 28th 2010, 06:29 AM
lex3
Pythagorean identities
Hi, I just learn about Pythagorean identities.
As i know that cos^2θ + sin^2θ = 1
but what is the work out to get 1? and why 1?

Thanks.
• Apr 28th 2010, 08:30 AM
kompik
Quote:

Originally Posted by lex3
Hi, I just learn about Pythagorean identities.
As i know that cos^2θ + sin^2θ = 1
but what is the work out to get 1? and why 1?

Thanks.

Consider a right triangle like here, i.e., the hypothenuse is denoted by h, opposite side is a and adjacent side is b.
Then:
sinθ=a/h
cosθ=b/h
and you know from Pythagorean theorem that $a^2+b^2=h^2$.
So if you calculate $cos^2\theta+\sin^2\theta$, you get
$cos^2\theta+\sin^2\theta=\frac{a^2}{h^2}+\frac{b^2 }{h^2}=\frac{a^2+b^2}{h^2}=\frac{h^2}{h^2}=1.$

You can even simplify this by rescaling the triangle so that h=1. (In case you're familiar with unit circle definitions of trigonometric functions, you should know, what I mean.)

BTW you have a whole article about this identity at wikipedia.
• May 4th 2010, 03:02 AM
lex3
Oh, now i understand.
Thanks mate!